Not sure if the ski's have a EGR Valve on them but would think they do for emissions, (Exhaust Gas Recirculation Valve) On car's these can stick and fail causing all of the problems listed above, what it does it put to much spent exhuast back in the system starving the motor for combustiable air, making the engine miss and sputter and have low power. This could be the cause! In auto's we use sea foam and induce it into the engine threw a vacume line, basically smoging the engine, once we have about a can sucked into the engine we let it sit for up to a hour, this will help remove the carbon inside the engine, then we restart, now a engine highly carboned up will smoke alot, and i mean alot! once it gets warmed up it will go away but may scare you on how much it smokes, and engines that have run ethonal fuel will really smoke heavly. Sea Foam will help to remove carbon from valves, exhaust, egr's and remove deposits from catalatic converters, this may help but it shouldn't hurt anything, just go slow when sucking it into the system, you will need help keeping the engine running as you induce it in the engine keeping the revs up so it won't die.
On car's the egr valve is controlled by the ecm, but not sure how of if its controlled on the honda engine in our ski's I think it may be controlled by vacume from the motor?? If anyone know's or has a shop manual look it up and let me know. I'm thinking this may be the cause. (NOTE: Stay away from ethonal blended fuels, on cars that run ethonal blended fuels we almost always have to sea foam them from carbon buildup!) Don't know why just know we do! And not trying to knock ethonal in anyway just know some things run differently on the stuff.